{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RBSRWC3J465DPFDMGKYWG74QTT","short_pith_number":"pith:RBSRWC3J","canonical_record":{"source":{"id":"1206.1801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-08T15:52:53Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"66d8705b26f285fe6e2a36831e29ef381f0828c6264d090211ef89d053a0ed9d","abstract_canon_sha256":"925e91eb4eacdbe77f67405a56ce17826bb89b25cfdb9f0014fac49817a42448"},"schema_version":"1.0"},"canonical_sha256":"88651b0b69e7ba37946c32b1637f909cd9b1c535ce38ebabf26f67f8b17ae14f","source":{"kind":"arxiv","id":"1206.1801","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1801","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1801v1","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1801","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"RBSRWC3J465D","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RBSRWC3J465DPFDM","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RBSRWC3J","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RBSRWC3J465DPFDMGKYWG74QTT","target":"record","payload":{"canonical_record":{"source":{"id":"1206.1801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-08T15:52:53Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"66d8705b26f285fe6e2a36831e29ef381f0828c6264d090211ef89d053a0ed9d","abstract_canon_sha256":"925e91eb4eacdbe77f67405a56ce17826bb89b25cfdb9f0014fac49817a42448"},"schema_version":"1.0"},"canonical_sha256":"88651b0b69e7ba37946c32b1637f909cd9b1c535ce38ebabf26f67f8b17ae14f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:55.404506Z","signature_b64":"eCVIEH5yfkmhAg1RXm2RCPXmTDaQxrAuEvV0ppkd4RWHp0VNRFrYO8sRxgrZlPz3EvVuSLVAOLopJyNsGEsaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88651b0b69e7ba37946c32b1637f909cd9b1c535ce38ebabf26f67f8b17ae14f","last_reissued_at":"2026-05-18T03:53:55.403773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:55.403773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.1801","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LW39Pnh9OLU2AwncRp7qSFOXVG0h7JVu/1KOfq6B5tUxZ0wwTFb8pDTrQYiKNQcely2blelpkMw/LXHX5gp0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:58:04.811037Z"},"content_sha256":"2947341f640562bafcb5df01aa237eb38b9c509eff4504a49bf60a3c909322b1","schema_version":"1.0","event_id":"sha256:2947341f640562bafcb5df01aa237eb38b9c509eff4504a49bf60a3c909322b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RBSRWC3J465DPFDMGKYWG74QTT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On an inequality for the Riemann zeta-function in the critical strip","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Sadegh Nazardonyavi, Semyon Yakubovich","submitted_at":"2012-06-08T15:52:53Z","abstract_excerpt":"By using new power inequalities we give an elementary proof of an important relation for the Riemann zeta-function |\\zeta(1-s)| <= |\\zeta(s)| in the strip 0< Re s<1/2,\\ |\\Im s| >= 12. Moreover, we establish a sufficient condition of the validity of the Riemann hypothesis in terms of the derivative with respect to Re s of |\\zeta(s)|^2 and conjecture its necessity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1801","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RL61IxBwTFboeeptL2fOVuW5A7345zw7QSaLDc4fQv2q4/UxE/UxFAUI2yedrT06aBqAP7/cd7Y07eolPaMjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:58:04.811397Z"},"content_sha256":"a8241c0b04c942e4bfc1c0a9cc21c630ff0831b85157796f1169c190c40543d9","schema_version":"1.0","event_id":"sha256:a8241c0b04c942e4bfc1c0a9cc21c630ff0831b85157796f1169c190c40543d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBSRWC3J465DPFDMGKYWG74QTT/bundle.json","state_url":"https://pith.science/pith/RBSRWC3J465DPFDMGKYWG74QTT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBSRWC3J465DPFDMGKYWG74QTT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T10:58:04Z","links":{"resolver":"https://pith.science/pith/RBSRWC3J465DPFDMGKYWG74QTT","bundle":"https://pith.science/pith/RBSRWC3J465DPFDMGKYWG74QTT/bundle.json","state":"https://pith.science/pith/RBSRWC3J465DPFDMGKYWG74QTT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBSRWC3J465DPFDMGKYWG74QTT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RBSRWC3J465DPFDMGKYWG74QTT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"925e91eb4eacdbe77f67405a56ce17826bb89b25cfdb9f0014fac49817a42448","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-08T15:52:53Z","title_canon_sha256":"66d8705b26f285fe6e2a36831e29ef381f0828c6264d090211ef89d053a0ed9d"},"schema_version":"1.0","source":{"id":"1206.1801","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1801","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1801v1","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1801","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"RBSRWC3J465D","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RBSRWC3J465DPFDM","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RBSRWC3J","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:a8241c0b04c942e4bfc1c0a9cc21c630ff0831b85157796f1169c190c40543d9","target":"graph","created_at":"2026-05-18T03:53:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"By using new power inequalities we give an elementary proof of an important relation for the Riemann zeta-function |\\zeta(1-s)| <= |\\zeta(s)| in the strip 0< Re s<1/2,\\ |\\Im s| >= 12. Moreover, we establish a sufficient condition of the validity of the Riemann hypothesis in terms of the derivative with respect to Re s of |\\zeta(s)|^2 and conjecture its necessity.","authors_text":"Sadegh Nazardonyavi, Semyon Yakubovich","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-08T15:52:53Z","title":"On an inequality for the Riemann zeta-function in the critical strip"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1801","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2947341f640562bafcb5df01aa237eb38b9c509eff4504a49bf60a3c909322b1","target":"record","created_at":"2026-05-18T03:53:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"925e91eb4eacdbe77f67405a56ce17826bb89b25cfdb9f0014fac49817a42448","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-08T15:52:53Z","title_canon_sha256":"66d8705b26f285fe6e2a36831e29ef381f0828c6264d090211ef89d053a0ed9d"},"schema_version":"1.0","source":{"id":"1206.1801","kind":"arxiv","version":1}},"canonical_sha256":"88651b0b69e7ba37946c32b1637f909cd9b1c535ce38ebabf26f67f8b17ae14f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88651b0b69e7ba37946c32b1637f909cd9b1c535ce38ebabf26f67f8b17ae14f","first_computed_at":"2026-05-18T03:53:55.403773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:55.403773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eCVIEH5yfkmhAg1RXm2RCPXmTDaQxrAuEvV0ppkd4RWHp0VNRFrYO8sRxgrZlPz3EvVuSLVAOLopJyNsGEsaCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:55.404506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.1801","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2947341f640562bafcb5df01aa237eb38b9c509eff4504a49bf60a3c909322b1","sha256:a8241c0b04c942e4bfc1c0a9cc21c630ff0831b85157796f1169c190c40543d9"],"state_sha256":"90eb33516c3a4305814378c037a42464262ba486e7f0b21e78289fa1ef5386e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7J52LCFlMsxr8rIvDXqM9Vp6wh3lDg1OAtTqDwhFSbeMTJAOOK48zRkV3g3Fe6qWRBG1BQ1I3d46aCM6eicxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T10:58:04.813598Z","bundle_sha256":"ccb620683cb78acf91977cc2a92753f7d25fcf3a465c9a0518550882c7f316a4"}}